Question: What causes our perception of time to change when we’re actively doing something compared to when we’re not doing anything?

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 What causes our perception of time to change when we’re actively doing something compared to when we’re not doing anything?

When you are actively doing something that makes your mind preoccupied so you aren't focusing on the time or how long something would take. Alternatively when you are doing nothing and time seems to stretch on and on it is because you have nothing to focus on so you become aware of how long a minute actually is.


Question: If any distance can be halved, at what point do you stop touching something?

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 If any distance can be halved, at what point do you stop touching something?

You're never touching anything - you are just as close as possible to it. The sensation you feel is effectively the force of the atoms "pushing back" against your fingers (and your fingers' atoms "pushing back" against the atoms in whatever you are touching). Think of it a bit like how two magnets push against each other, but much much stronger.


Question: How exactly does currency “move” between banks, individuals, companies, etc. when processed electronically and without the use of any actual physical currency (cash)?

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 How exactly does currency “move” between banks, individuals, companies, etc. when processed electronically and without the use of any actual physical currency (cash)?

Ahoy, matey! Yer not alone in askin', and kind strangers have explained: 1. [ELI5: What happens when money is digitally transfered from one bank to another? Is the money later picked up to be stored there? Or is there some sort or digital I.O.U. involved? ]( URL_1 ) 1. [ELI5: Electronic Funds Transfers ]( URL_0 ) 1. [ELI5: How do wire transfers work? ]( URL_3 ) 1. [ELI5: What really happens when banks transfer money? ]( URL_2 )


Question: How can nuclear fussion and nuclear fission both produce energy?

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 How can nuclear fussion and nuclear fission both produce energy?

If you imagine the amount of energy that fusing an atom into "the next" atom gives off, you'll find a lot for the light elements, with reducing payoff as you get heavier, until you hit iron. Once you hit iron, it goes negative. Fusion stops giving off energy but instead requires energy. It is for this reason that all atoms heavier than iron were necessarily forged in supernovae and similar. But because of this, that means if we can split open heavy atoms, we can get out that extra energy required to make the atom in the first place. Same deal with gasoline, just on the atomic scale, not molecular scale.


Question: What part of your Appendix bursting is actually dangerous to humans?

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 What part of your Appendix bursting is actually dangerous to humans?

Uh, all of it? You don't want your organs to burst. Pretty much any organ, if it bursts, is going to be life-threatening. Regarding the appendix specifically: for one thing, it means that the blood and lymph vessels that supply the appendix are now severed and spilling blood/lymph into your abdomen. For another thing, appendices burst because they're infected. They're filled with harmful bacteria, and when they burst they spill those bacteria into your abdomen to go infect other parts of the body. For another thing, the appendix is part of the digestive system, which means it's filled with acid and bile and other corrosive fluids. When those spill out into the body, they start digesting it.


Question: Can't you simply guess a PaySafeCard pin since it only contains numbers?

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 Can't you simply guess a PaySafeCard pin since it only contains numbers?

In principle, yes. But how many valid PINs exist at any time? Let's be very optimistic and guess 1 billion. There are 10 quadrillion possible 16-digit PINs, so you have a 1 in 10 million chance of guessing a valid PIN. That puts it in the same ballpark as guessing the winning lottery numbers, and there are probably far fewer than a billion active PINs.


Question: How can Google display and monetize things like article snippets and images under copyright?

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 How can Google display and monetize things like article snippets and images under copyright?

Copyright laws allow for certain types of “fair use”, such as short clips from videos or songs to be played. A great example would be a Youtuber showing clips from somebody else’s video (or a news report) and adding their commentary about the other video. I’d imagine partial text from an article or a reduced-size photo fall under these rules too. Google is not reproducing the entire work in its original format or quality, and a main feature of their search engine is not only telling you where the item came from, but helping you navigate to their website so you can view it there. I think they did have to change their image search function a few years ago— it used to link directly to images but now links to the page that contains the image. This allows the whoever created the image to show their ads to profit from it, as well as present it with whatever additional context or info they include on their webpage.


Question: Why haven't Saturn's rings coalesced into much larger moons?

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 Why haven't Saturn's rings coalesced into much larger moons?

Basically, the junk that makes up Saturn's rings are too close to Saturn. They do occasionally clump together and start forming masses, but the gravitational forces exerted by Saturn are too strong where they are, and the clumps of dirt are squished and stretched until they fall apart. We actually even see that the rings furthest from Saturn do have larger and larger clumps. But none of them are far enough away to form anything big enough to be a natural satellite (moon). Here's a link to a not-so-great Wikipedia article. It is called the [Roche Limit] ( URL_0 ).


Question: If University of California gets 13% of revenue from student fees, but spends 14% on financial aid, why can't tuition just be cut to zero?

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 If University of California gets 13% of revenue from student fees, but spends 14% on financial aid, why can't tuition just be cut to zero?

So you’re saying that students cost 27% of their revenue... Why can’t they use the 14% of X total revenue to pay 27% worth? It might be helpful to work with real numbers. Also financial aid typically comes from banks and the govt (plus various scholarship sources). So I’d question when you say it “spends”


Question: why countries with weak currency don't remove multiple zeroes off their money to make it worth more?

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 why countries with weak currency don't remove multiple zeroes off their money to make it worth more?

It happens, but it doesn't make the money worth more. It is only a cosmetic change that turns larger numbers into smaller ones, but it does not change anything about the underlying value. Turkey did just that in 2005. They replaced all their banknotes with new ones that had 6 zeros less on them. 1,000,000 old Lira would be worth 1 New Lira. Prices in shops and wages and bank accounts and debts would have 6 zero lobbed of them to go along with the new money. It didn't mean that anyone in turkey suddenly was any poorer or richer than before. Nothing changes on a practical level. The new currency just looked less ridiculous and was easier to handle. The main benefit that the government had been after to make a statement. the currency had undergone some very big inflation which is why they ended up with such large numbers, and the move was supposed to signal that this was now over and they were in normal times now. It was supposed to boost confidence in the currency that further inflation would be limited. This also shows why more countries aren't doing it. For example the Japanese Yen started out being worth exactly the same as the US dollar when it was crated (they were both copies of the Spanish dollar, the pieces of eight from pirate lore.) Since those days both Japan and the US have undergone some inflation. Japan thanks in part to losing WWII has undergone a lot more though. 1 US dollar today is worth more than 100 Yen and prices expressed in Yen all seem a lot larger than ones expressed in Dollars pound or Euro. Japan could lop of two zeroes of their currency to get it more in line with other world currency, but frankly they don't need to. The two extra decimal places are still manageable and Japan doesn't have to prove anything to anyone about the stabilize of their currency. Anyone looking at the Yen today will see the scars of past inflation on it, but also know that it is in the past. With Turkey observer had no such confidence and thus the government had to artificially boost it. Other than the practical aspects of keeping price tags short revaluating your currency like that is something you do when you need to project strength that people don't think you have. It might be seen as a sign of weakness itself. There is also the fact that switching out all your banknotes and coins for new ones like this will be an expensive undertaking and one not made unless there is some very good reason. Prosperous countries only undertake such projects when there is a clear benefit like all the Euro countries switching to a common currency or to a lesser degree when the British a few decades further back decided to go decimal with their coins.


Question: if you're standing on the back of a truck headed North at 100 mph, and you throw a baseball South at 100 mph, would the baseball appear to fall straight down to someone watching from the side of the road?

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 if you're standing on the back of a truck headed North at 100 mph, and you throw a baseball South at 100 mph, would the baseball appear to fall straight down to someone watching from the side of the road?

Yes. Speed is always relative to some point of reference. To someone standing on the truck the ball shoots off against the direction of travel at high speed. To someone stationary near the point where it's thrown it falls straight down. [Here's Mythbusters doing this experiment with a soccer ball fired from an air cannon]( URL_0 ).


Question: Why most of round trip tickets are cheaper than one way?

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 Why most of round trip tickets are cheaper than one way?

Domestically they're not. One way is usually a bit over half as much as a round trip flight. International is a different story. If an airline flies you into a country and then that country refuses to allow you to enter, then *regardless of why you were refused entry* the airline needs to pay to fly you back. There are also very, very few people who fly international one way, so airlines are extremely suspicious about anyone who does. Because of the risk that international one way passengers pose to airlines, as well as their rarity, airlines just assume that a high percentage of such passengers will be rejected by the destination country and bake the weighted average cost of a return ticket into the one way ticket price.


Question: Why do colors disappear when you zoom in with a microscope?

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 Why do colors disappear when you zoom in with a microscope?

In order to see something with a light microscope, you need to have a very, very thin cross-section. It has to be thin enough for light to be able to pass through it (for the most part). Otherwise, the image under the microscope would appear opaque or black. But a small cross section means that there's not really that much material and/or pigment to add color to the light. Look at a drop of water or a very shallow puddle of water on a white background. Not very much color is there? But look at the ocean from space. All that water is a rich, deep blue. It's the same with a microscope. A carrot may look deep orange with the naked eye, but when you slice a thin enough piece off to see it under a microscope, it's a very pale orange if any color can be [seen at all]( URL_0 ). If you're talking about images from an electron microscope, then an EM doesn't really see color. An EM uses electron beams and their reflection off of things for a computer to render a 3D image of what something looks like. It's like a blind person examining an object with his hands. Sure he can tell you precisely what shape and texture the object is, but he has no clue what color it is. An EM is the same way.


Question: Why does soap smell good but taste bad?

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 Why does soap smell good but taste bad?

There are a few reasons, but in my opinion one of the main reasons has to do with evolution. Many things found in nature that are alkaline (having a pH higher than 7) are poisonous to humans so naturally we have evolved to find these tastes repulsive. Since soap is highly alkaline, it tastes bitter.


Question: Why do very light objects take a great deal of force to throw, like very heavy objects?

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 Why do very light objects take a great deal of force to throw, like very heavy objects?

because of air resistance. a moving object has energy which is a product of its mass and speed. when the object travels through air, it loses some of that energy in order to push the air out of the way. because of its low mass a light object has less energy and runs out of it more quickly than a heavy object.


Question: Why does in private browsing let you view more articles on a website that restricts you to a certain amount of free articles per month when you've gone past the limit of free articles?

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 Why does in private browsing let you view more articles on a website that restricts you to a certain amount of free articles per month when you've gone past the limit of free articles?

Before I answer this, let’s first answer the question how websites know you’ve read a certain amount of articles in the first place. They do this through a method called caching. In simple terms, it is somewhat of a temporary storage in your computer so when you visit the website again, you don’t have to request everything again. This improves page speed since you only need to ask what is new and up to date. Now, when you browse privately, the browser doesn’t store the cache. I mean, they do but once you close the browser, it’s gone. Also, when you browse privately, the cache from your non-private browsing isn’t carried. It’s assumed you’re starting from scratch. That’s the reason why you have to sign in to every website in incognito even though you already signed in. EDIT: As /u/krystar78 pointed out, apparently it isn’t cache but cookies.


Question: How sports are able to keep such high viewership without any change while esports games need to change constantly to stay relevant?

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 How sports are able to keep such high viewership without any change while esports games need to change constantly to stay relevant?

Video games exist in a consumer bubble. Sports don't. Sports don't change. Sports don't get re written, or replaced. You can't change physics. And to get good at a sport athletes spend hundreds of thousands of dollars and for some sports their entire lifetime getting good at it. Then take a new game. It's going to be replaced by another new engine with better graphics that takes what that game did, but does it better. People want esports to be taken seriously like real sports. It's competitive and entertaining. But something new comes along all the time. Even the most popular, intensive game like dota, hasn't existed a fraction of the time of a lot of the popular sports. So it can't have the same trans generational appeal. Sports largely exist as entertainment. That's why they have monetary value (advertisement potential). But they exist in our society for complex reasons like mastery, didactis and some believe a replacement for war. Esports will always struggle to be in the same area because they can't natually/quickly appeal to society outside those who play the game. There isn't a physical component to it either. Your grandfather can't sit there and watch you play and be impressed the very first time he see's it. But he can watch someone basically defy physics on the tv and be impressed the very first time. He can make sense of what he's watching. And again, 10 years from now that game will be replaced; there never will be a catch up period. Edit: so this is what it's like to be one of the first commentators on a thread. Cool. Hi mom


Question: What are the root causes of anxiety disorders?

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 What are the root causes of anxiety disorders?

Both. Both is generally accepted for a majority of diagnosable mental disorders. It’s anxiety disorders, your body gets stuck in a pattern of overreacting to stimuli. You can have a genetic predisposition to be more anxious or to have a low threshold for anxiety. Couple that with some environmental stressors that push you past your threshold and that’s how disorder could appear. Of course, that’s only one way of many, and people have different thresholds based on genetics. It might take someone only a few environmental stressors or a lot before the body gets “stuck” in a dysfunctional pattern. AND trauma and stress are totally subjective. What may be minimally stressful for one human may be majorly stressful to someone else. EDIT: I hope that made sense because I just got home from work 🙈


Question: Can anyone explain to me the chain rule? I'm kinda doing some self study ryt now, and i'm having a hard time with it. I think i already have a good background with the basic rules, but i am confused when some problems contains mix rules: < <

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 Can anyone explain to me the chain rule? I'm kinda doing some self study ryt now, and i'm having a hard time with it. I think i already have a good background with the basic rules, but i am confused when some problems contains mix rules: < <

the chain rule is something you use when you want to differentiate "difficult" (nested) equations. you can use it to calculate (x+1)^3 without having to expand it into x^3 +3 x^2 + 3 x + 1 this is one of the easier examples, when you're faced with sqare roots, trigonometric (sin/cos) or exponential functions it is often very difficult to expand it into a simpler form to differentiate. sin (2x) for example is also a "nested" equation it is "sinus of (two times x). so what you do is substitute the "inner" part of the equation. (x+1)^3 becomes u^3 sin (2x) becomes sin (u) sqrt (x^3 - x^2 + 7) becomes sqrt (u) (you can also make substitutions like x^4 +x^2 +1 becomes u^2 +u+1) important: after the substitution you should not have an "x" left in your equation, only "u"s and different powers of "u" (obviously you can also choose a different letter), like u^2, sqrt (u), etc. now you take the much easier equation with the "u" parameter and differentiate it. taking the sin(2x) example (because it's easy but not trivial): this gives you sin'(u) = cos (u) now you gotta multiply that with the derivation of the "inner" part, because we want to know how what happens to our "u" when we derive it. here our "u" is just "2x" so u' = 2 and thus the result is sin' (2x) = 2 cos (2x)


Question: Why, when you start laughing, every other joke, as silly as it may seems in a normal context, seems absolutely hilarious?

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 Why, when you start laughing, every other joke, as silly as it may seems in a normal context, seems absolutely hilarious?

The part of your brain that makes you laugh has an activation threshold, but once it's active, well, it is easier to keep it active. Think of it like turning on a car with an half-dead battery: hard to do, but once it is running, it keeps going. It's actually like this with many other things, many other moods. Think of sexual arousal.


Question: - Why are there unsolved mathematical equations? Who wrote them and how do they know if they are solvable or not?

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 - Why are there unsolved mathematical equations? Who wrote them and how do they know if they are solvable or not?

So...you should note that mathematical problems and mathematical equations aren't inherently the same thing. An equation is basically just two sets of algebraic quantities that have an equal/greater than/less than sign between them. Some of these equations are inherently not solvable because they have self-contradictory answers. For example, let's say you have the equation; 1/(x + 3) + 1/(x - 3) = 6/(x^2 - 9) You can manipulate it (multiply both sides by "(x + 3)\*(x - 3)") to get the following; x + 3 + x - 3 = 6 or; 2\*x = 6 or; x = 3 But that doesn't actually work, because if you plug x = 3 back into the original equation one of the two terms on the left side of the equals sign gives you a 1/0 situation, which means that x = 3 is essentially not "allowed" to be an answer. Thus, the equation has no solution, making it unsolved. For unsolved *problems*; those are basically just mathematical statements that we can't quite figure out if they're true or not. For example, there's the Collatz Conjecture; pick a number, and then perform the following operations; 1) If it's even, divide it by 2. 2) If it's odd, multiply it by 3 and add 1. Then feed the resulting number back in, and again, and again. Doing this, you'll (probably) end up with a repeating sequence of 4, 2, 1, 4, 2, 1, etc. No matter what your starting number is, you always seem to end up in this pattern because *eventually* you wind up with some number 2^N and the whole thing collapses. The problem is that we can't figure out how to prove that it's explicitly true for all numbers; we can only observe that it hasn't been disproven yet, which is not good enough for mathematics. Thus, the problem is unsolved.


Question: Before phones were popularized, how were the police informed of a crime taking place?

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 Before phones were popularized, how were the police informed of a crime taking place?

Walking to the sherrif's office/police station and letting them know. Some areas also had police call boxes (Yes, like the Doctor Who thing) in high traffic areas like parks that would connect you with emergency services, in America at least you can still occasionally see call boxes around although I've seen more fire call boxes than police. For the most part though, fast police response wasn't a thing.


Question: Why do streaming providers supply different content to different countries? Can't they just provide the same content to everyone?

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 Why do streaming providers supply different content to different countries? Can't they just provide the same content to everyone?

Different countries have different laws in regards to content shown, tv regulations and licensing rights. Netflix US has Arrested Development S5 but Netflix AUS doesn’t due to Foxtel having first airing rights. Some programs are banned from certain countries for religious reasons or what is portrayed culturally. While some shows have to be censored or edited to comply with some countries which the streaming service may not have access to. All in all if a streaming provider breaches a countries laws in regards to their content, they are held responsible and have to face legal repercussions


Question: What's the difference between white and brown sugar, and why does more brown sugar make cookies so much softer?

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 What's the difference between white and brown sugar, and why does more brown sugar make cookies so much softer?

White sugar is brown sugar after being processed to take molasses out of it. Originally, brown sugar came first, but most commercial brown sugars are actually made from adding molasses back in to the white sugar, rather than just leaving it in its first stage. Probably because it's easier/cheaper for a company to get a hold of white sugar post-processing than to nab it in its raw form. Brown sugar makes things softer because the added molasses adds moisture to the baked end result.


Question: Why are metals attracted to magnets?

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 Why are metals attracted to magnets?

**tl;dr - electrons are little magnets, and materials are magnetic based on how their electrons and atoms are arranged** Electrons are magnetic. They have a quantum property called intrinsic magnetic moment, which makes them act like very small magnets. Atoms *can be* magnetic. Electrons in atoms tend to group in pairs, orbiting in such a way that their magnetic moments cancel out, which means only atoms with half full, or nearly half full, outer shells (Iron, Nickel, Cobalt, etc) are magnetic. Lots of magnetic atoms together in a material *might be* magnetic. If the overall crystal arrangement of the atoms in a material means that the magnetic moment of its atoms point the same way, the material will be magnetic. If not, you may be able to run a magnet over the surface of a material to temporarily align the magnetic moments of the atoms, magnetising the material.


Question: How do speakers perfectly recreate the specific timbre of different sounds, like human voices and instruments?

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 How do speakers perfectly recreate the specific timbre of different sounds, like human voices and instruments?

Three parts to the how: 1. The microphone that records voices and instruments (like an orchestra) is very similar to a (very small) speaker, and functions in reverse: the air vibrations push the cone and it creates electromagnetic oscillations. The EM oscillations are amplified and then sent to speakers, which convert them back into air vibrations by vibrating the cone. Your speakers are able to emulate the vastly different types of noise because the microphone picks up the vastly different types of noise, and both devices use the exact same mechanism. 2. Sound is waves. Waves add up. Make ripples in a pool and you'll see: if you dive bomb you'll make one big wave (that's like bass sounds) and if you also splash your hands around you'll make some smaller waves (like high pitched sounds), and your friend waiting at the other side of the pool will see one big wave with smaller ripples on top (bass and high pitch added together). Look at [this picture]( URL_0 ), bottom line is bass (low frequency) with treble (high frequency) compounded. [This image]( URL_1 ) is multiple (pure tone) waves combined into a complex sound - the bottom left wave is a complex sound made up by adding together the more simple waves in the rest of the image. 3. Your brain is what distinguishes between the various voices and instruments. Just like you can see multiple colors and shapes in an image, your ears pick up the complex sounds and then your brain automatically decomposes the complex wave back into individually recognizable sounds. The electronics, the microphone and the speakers, they don't do anything, they just amplify whatever they pick up. Your brain does all the work at recognizing and understanding sounds. How? I don't think we know. It's amazing.


Question: Why do nosebleeds happen out of nowhere?

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 Why do nosebleeds happen out of nowhere?

On the inside of your nose you have blood vessels very close to the surface. For a variety of reasons some may be weaker then others. High blood pressure thru exercise, and even diet can raise your pressure just enough to make it burst. There are also medical reasons and nose bleeds can be a symptom.


Question: How do powerline adapters work? What is the connection between powerlines and networks?

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 How do powerline adapters work? What is the connection between powerlines and networks?

The power lines in your house are just copper (usually) cables which are designed to carry mains voltage to power devices in your house. While that's what they're \*designed\* to do, it doesn't stop them carrying other kinds of signal as well, so what a powerline network adapter does is to convert the network traffic into a high-frequency signal carried along the mains wiring; at the other end the adapter filters out the noise from the mains current and extracts the network signal. How well this works depends on how good your wiring is and how far apart the two adapters are.


Question: What is the difference between different soaps?

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 What is the difference between different soaps?

If you'll forgive me the conceit of quoting myself: > Because removing dirt, grime, and oil isn't the only characteristic you want, depending on what you're cleaning. Various kinds of detergents/soaps have secondary characteristics, and which one is good for which task is largely dependent on those secondary characteristics. > Just for dishwashing, compare dish detergent to diswasher detergent. The latter is better at stripping fats off surfaces than the former - not least because it's pretty aggressively caustic (in comparison to other household chemicals, at least). It actively dissolves fats, rather than just helping hot water emulsify them. This makes it materially harder on your skin (which is covered in and made of fats), and much more dangerous than dish detergent if ingested (dishwasher detergent will burn your mouth and throat, dish detergent will give you diarrhea). > Meanwhile, dish detergent includes foaming agents, because people like suds when they wash dishes. Your dishwasher, however, does not at all like suds - put dish detergent in your dishwasher, and you will come home to a foam party. Which is fun, unless you're the one who has to clean it up. > Which brings us to a reason not to use dish detergent for other household cleaning - cleanup. Because dish detergent is designed to wash dishes, it designed with the assumption that the things it's cleaning will be rinsed off in plenty of water. Very little effort is spent trying to make sure that no film is left on something if you don't rinse it. > This is poor design for washing - say - windows, where you typically do not run a lot of water over the glass after cleaning it. So for windows, you use a cleaner which isn't as good at stripping dirt, but is very good at drying without leaving a film behind. > The problem is worse for things like bodywash, which frequently are designed to leave a residue on your skin (to moisturize). That's not a residue you want on your dishes, floors, or windows. (You probably also don't want your dishes to smell like they and a mountain are in a band together) > Bodywash is also designed to be much less aggressive at removing fats - most of the stuff you want to wash off in a typical shower is either particulate or water soluble. And again, you're covered in and made of fats; you don't want to attack them too hard. Which is why if your hands are covered in grease (say from working on a car), you're best served by using Goop or similar to clean them off. > Laundry detergent has its own set of design goals, which also don't align very well with various other cleaners. Laundry detergent needs to not aggressively attack the dyes or fabrics it washes, but it also needs to work for removing soils that are fat-based. But it has the advantage that it both gets a relatively long period to work (the whole wash cycle, including "soak" time), and there is friction being applied (through agitation), rather than just hot water. So the better laundry detergents incorporate enzymes to attack fats, instead of being particularly caustic. > All that said, you probably could use dish detergent for most of your cleaning needs, it just wouldn't be as good as the various other cleaning agents we typically use. You can (obviously) hand wash your dishes in it. And assuming you don't have a high efficiency washing machine, the foaming likely wouldn't get too out of hand - though you'd have more stains that wouldn't go away, and you would need to be more careful about separating clothes by color family. If you used it in the shower, you'd need to be a bit more careful dosing it out (it's more concentrated than bodywash), and your skin would be pretty dry, but you'd be clean. If you did a good enough job wiping down all the other surfaces in your house with a clean, damp rag after washing them and then meticulously wiped them dry, you could avoid having a film on everything. > So if the goal was to reduce your detergent/soap inventory to just one product, I would recommend dish detergent. Specifically, blue Dawn. It's probably the best all-rounder in the average household.


Question: How do rotation matrices work in computer graphics?

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 How do rotation matrices work in computer graphics?

If you have some time, I highly reccomend watching [3b1b's series on Linear Algebra]( URL_1 ). At least watch just [the video on Linear Transformations]( URL_0 ) . Which explains why transformation matrices look the way they do (including rotation matrices). The rotation matrix tranforms a vector (x,y) by rotating it θ radians. But here's another way of thinking about it: The columns of the matrix tell you where the basis vectors land *after* the transformation. This is true in general, not just rotations. In 2D you have the two standard basis vectors: (1,0) and (0,1). So if you want a rotation by 90 degrees, then the basis vector (1,0) turns into (0,1). And the basic vector (0,1) turns into (-1,0). So the matrix that describe a 90 deg rotation looks 0 -1 1 0 However in genera we want to rotate by θ. If you want to rotate the vector (1,0) by θ, then after the rotation the coordinates of the vector will be (cosθ, sinθ) < -- This comes from the unit circle. This is the first column of the rotation matrix. Similarly, if you rotate (0,1) by θ, the resultign coordinates is (-sinθ, cosθ) which is the second column of the matrix.


Question: if I place both waters into a bucket from where the two oceans meet but don’t mix, why do they mix just fine in the bucket?

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 if I place both waters into a bucket from where the two oceans meet but don’t mix, why do they mix just fine in the bucket?

The idea of "two oceans meet but don't mix" is more or less a myth. Most of the pictures of this you see on the Internet are at rivermouths or headlands, where a sharp contrast between water types is visible ... but it mixes away pretty quickly. Tom Scott did a video on this recently. URL_0


Question: Why is the production of iron atoms a sign that a star is dying?

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 Why is the production of iron atoms a sign that a star is dying?

A star is big and shines bright. Most stars have hydrogen, element #1. Stars are so big and strong that they can squeeze four hydrogen atoms together to make element #2: helium. When stars fuse atoms together, usually it releases energy that makes the star shine bright. The star keeps doing this and they can make all sorts of elements, including #26: iron. But that takes a lot of energy. When a star makes iron, it uses more energy to make iron than iron makes the star shine. Making iron makes the star tired, and it will die for it. Edit: a star is big and shines bright.


Question: Why is there demand for stocks that don't come with dividends?

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 Why is there demand for stocks that don't come with dividends?

"is there any point in owning a share that doesn't pay dividends besides the possibility at selling it for a profit?" No. If a stock doesn't pay out dividends, it's called a growth stock, which is a stock intended to keep your money liquid and hopefully appreciate in value. The company gets the initial IPO. The thing about dividends is that it's not free magical money. The dividend payout actually drops the value of the stock equal to the amount of dividends paid. The company doesn't get anything more than the initial IPO here either.


Question: Why/how do our eyes "lose focus" and get blurry? What's happening?

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 Why/how do our eyes "lose focus" and get blurry? What's happening?

Basically it takes effort to focus your eyes, when you gaze off into the distance, not really looking at anything, your eyes realize they don't have to do work, and get a bit hazy. HOW this works is a bit more interesting, your eye lens is flexible, (even though you might have thought it was hard in that cow eyeball you dissected in high school) and is able to change shape by consciously or unconsciously changing the muscles in your eye. A rounder lens is able to focus on closer objects, as seen [here:]( URL_1 ) and a flatter lens is able to focus on things that are further away as seen [here:]( URL_0 ) EDIT: I will try to answer all your questions tomorrow, as I'm going to bed now.


Question: How do stocks go up or down?

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 How do stocks go up or down?

Its actually super simple. Person A wants to sell his stock. Current price is the last time someone traded that stock, lets say $25/share. Person A puts his stock up for sale for $26/share. Someone buys it. The new stock price is now $26/share. Now, if Person A can't sell the stock, and lowers his price, to lets say $24/share, and someone buys it, that's the new stock price, $24/share. It's all just simple supply and demand. If there is more demand to buy the stock than people selling, the price will go up. If there is less demand to buy the stock than people selling, the price will go down.


Question: How does the International Space Station(The ISS) gets their Oxygen supply? Does it gets refilled on a regular basis? How does it gets refilled and what is the capacity of their Oxygen tank?

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 How does the International Space Station(The ISS) gets their Oxygen supply? Does it gets refilled on a regular basis? How does it gets refilled and what is the capacity of their Oxygen tank?

Primarily via water electrolysis (running an electric current through water to break it down into Hydrogen and Oxygen), though they also get supply shipments from Earth every couple months. They also have a backup system that can generate oxygen by burning lithium perchlorate. Not quite sure what their storage capacity is though.


Question: How do stock prices and currency values go up and down?

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 How do stock prices and currency values go up and down?

The stock price you're referring to is actually the price of the last trade. It is a historical price – but during market hours, that's usually mere seconds ago for very liquid stocks. Whereas, the bid and ask are the best potential prices that buyers and sellers are willing to transact at: the bid for the buying side, and the ask for the selling side. But, think of the bid and ask prices you see as "tip of the iceberg" prices. For examples, a "Bid of 13.20 x200" is an indication that there are potential buyers bidding $13.20 for up to 200 shares. Their bids are the highest currently bid; and there are others in line behind with lower bid prices. So the "bid" you're seeing is actually the best bid price at that moment. If you entered a "market" order to sell more than 200 shares, part of your order would likely be filled at a lower price. The "Ask of 13.27 x1,000" is an indication that there are potential sellers asking $13.27 for up to 1000 shares. Their ask prices are the lowest currently asked; and there are others in line behind with higher ask prices. So the "ask" you're seeing is the best asking price at that moment. If you entered a "market" order to buy more than 1000 shares, part of your order would likely be filled at a higher price. A transaction takes place when either a potential buyer is willing to pay the asking price, or a potential seller is willing to accept the bid price, or else they meet in the middle if both buyers and sellers change their orders. Note: There are primarily two kinds of stock exchanges. The one I just described is a typical order-driven matched bargain market, and perhaps the kind you're referring to. The other kind is a quote-driven over-the-counter market where there is a market-maker. In those cases, the spread between the bid & ask goes to the market maker as compensation for making a market in a stock. For a liquid stock that is easy for the market maker to turn around and buy/sell to somebody else, the spread is small (narrow). For liquid stocks that are harder to deal in, the spread is larger (wide) to compensate the market-maker having to potentially carry the stock in inventory for some period of time, during which there's a risk to him if it moves in the wrong direction. Finally ... if you wanted to buy 1000 shares, you could enter a market order, in which case as described above you'll pay $13.27. If you wanted to buy your shares at no more than $13.22 instead, i.e. the so-called "current" price, then you would enter a limit order for 1000 shares at $13.22. And more to the point, your order would become the new highest-bid price (until somebody else accepts your bid for their shares.) Of course, there's no guarantee that with a limit order that you will get filled; your order could expire at the end of the day if nobody accepts your bid.


Question: How does dynamite work, and does it work differently than a hand grenade?

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 How does dynamite work, and does it work differently than a hand grenade?

The dynamite will not blast into a rock if placed next to it. The force is not pushed in any one direction. If a hole was drilled and it was placed inside. It would exert pressure against the rock in all directions. A hand grenade is made “pre seamed” and designed to fragment and create shrapnel. In all directions. The dynamite is set off by a blasting cap, I think most grenades use a burn time or piezo crystal?


Question: how do non-narcotic painkillers (acetaminophen, ibuprofen, etc.) work?

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 how do non-narcotic painkillers (acetaminophen, ibuprofen, etc.) work?

Mostly by treating the inflammation. Basically there's a chemical your body produces (cyclooxygenase or COX) that triggers inflammation by making another chemical prostaglandin. These non-narcotic drugs (also called Non Steroidal AntiInflmmatory Drugs or NSAIDS) or COX blockers. This stops the inflammation chemical from being made and reducing the pain caused by it. Narcotics affect your brain directly which is why your entire system is affected.


Question: If humans manufacture currency, why can't we manufacture more money and hand it out to the less fortunate /lower class?

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 If humans manufacture currency, why can't we manufacture more money and hand it out to the less fortunate /lower class?

Without something backing it, money is just paper. Economies are massive in scale, but not infinite. Each bank note is essentially a portion of a government's wealth. Printing more money, but not generating more wealth is simply dividing that wealth further among currently circulating notes, not creating more. Hyperinflation is basically that on steroids. Eventually you get to the point that the money isn't worth the paper it's printed on.


Question: You know how bees have to have a Queen - is the Queen bee born a queen, or when the queen dies does another bee transform into a queen? If so how does the hive decide who gets to be the queen bee?

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 You know how bees have to have a Queen - is the Queen bee born a queen, or when the queen dies does another bee transform into a queen? If so how does the hive decide who gets to be the queen bee?

/u/jotenha1 is incorrect. Any larva has the potential to be a queen. It's their upbringing that turns them into queens. They're raised in their own special section of the hive and are fed a lot of royal jelly. Royal jelly contains a protein called royalactin, which changes the larva's gene expression to cause her to become a queen. Recent studies suggest that it may also be the lack of being fed normal honey that causes the chosen larva to become a queen. The queen bee also releases pheromones to prevent worker bees from building more special sections in the hive for future queen bees. The queen bee's DNA and a worker bee's DNA are the same. The only difference is which genes are expressed. As for how the larvae are chosen to be queen, I'm not sure.


Question: How does surface tension work?

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 How does surface tension work?

Water molecules like to hang out with each other more than with air or other things that don't dissolve in it. The molecules don't bond together, but the hydrogen in one water molecule is attracted to the oxygen in another. (I'll skip the segue into electronegativity, polar bonds, and hydrogen bonding) In the center of a mass of water, this attraction doesn't matter since it's the same in all directions. At the surface, attraction isn't uniform and the molecules are pulled more strongly towards the base material and other surface molecules. This makes the surface more viscous than the material normally is and makes it more resistant to things moving through it. If you look closely at the bugs that walk on water, you can see that the water isn't flat where they touch it. Their weight does push the water under them down, but not enough to break the water molecules apart. This put the crater below the surface which creates a buoyant force pushing up on the crater surface and keeps the bug from sinking. Detergents and other surfactants have a part of their molecule that repels water and effectively put "holes" in the surface tension where the water molecules aren't attracted to each other. When the surface gets stressed, there are less bonds to share the load and the surface "breaks" at a lower value than plain water.


Question: Why are some people content living vicariously through others, while some people just get mad and jealous?

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 Why are some people content living vicariously through others, while some people just get mad and jealous?

I think you've got it wrong. People aren't "living vicariously" through others. They're either jealous (like you) or they feel happy that their friends experienced something interesting or fun. It's the fun and interesting things my friends have experienced which is why I want them as friends. If you feel mad and jealous at the positive things that happen to others, particularly your supposed friends, you might want to talk to a mental health specialist. It's not uncommon but it's certainly not good.


Question: What happens to the weight that you loose when on a diet?

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 What happens to the weight that you loose when on a diet?

You breathe most of it out as carbon dioxide, and pee some of it out as water. All of the energy we get from our diet is used to support cellular respiration. The input is sugar and oxygen, and the output is carbon dioxide and water. When you lose weight, you're forcing your body to raid its fat reserves, and convert the fat into sugars, which are then used to provide energy to all your cells.


Question: What would a person without colour blindness see if they wore a pair of colour blindness correction glasses?

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 What would a person without colour blindness see if they wore a pair of colour blindness correction glasses?

Enchroma lenses work by filtering out the color wavelengths that "get confused" by people with colorblindness, but don't filter out the other shades around them. A study of the Enchroma CX-14 lenses using people with normal color vision experienced what is known as a tritan defect, which has blues and violets as more green and dim, and purples are turned into shades of red. [Here is a picture taken back to back. The top one is with a normal lens, and the other is with an Enchroma lens.]( URL_0 ) some of the colors are more washed out in the original, but not in the Enchroma lens. Unfortunately, this image doesn't really have any purple or blues other than the verdigris on the statues to show that color change. Edit: [Here's another example showing a rainbow through the glasses and around them.]( URL_1 ) It appears as if the rainbow is turned from a gradient to the distinct bands, one red, one chartreuse, and one indigo, with small sections where they fade into each other.