blem</a>.)</li>
    </ol>
  </div>
    <p>If the vectors you found in the previous problem matched up
  with the direction vectors of the lines in <a href=
  "#cake-introduction">this problem</a>, you are doing things right.
  Partial derivatives of parametric functions tell us tangent
  directions. We can interpret this also in terms of motion.</p>

  <div class="problem">
    Consider the change of coordinates $\vec T(r,\theta) = (r\cos
    \theta, r\sin \theta)$.

    <ol>
      <li>
        <div class="