}-3y^2\\2x\end{bmatrix}$, and $D\vec F =
    \begin{bmatrix}0&amp;-3y^2\\2y&amp;2x\end{bmatrix}$. Also,
    $d\vec
    F=\begin{bmatrix}0&amp;-3y^2\\2y&amp;2x\end{bmatrix}\begin{bmatrix}dx\\dy\end{bmatrix}$.
    Remember that we can visualize a vector field by drawing arrows
    on the plane (for example, like wind velocities at every point
    on the plane). We can interpret this last equation as saying
    that if we are at a point $(x,y)$ on the plane, and we move a
    small distance away to $(x+dx, y+d