- Let $\vec F = (0,-10)$ and $\vec d = (3,2)$. Compute both $\vec F_{\parallel \vec d}$ and $\vec N = \vec F_{\perp \vec d}$.
- Draw the curve $u^2+v^2=1$ in the $xy$ plane using the change of coordinates $x=3u-1$ and $y=2v+4$. Give a Cartesian equation of the curve.
- Draw $\left(\frac{x}{3}\right)^2+\left(\frac{y}{5}\right)^2=1$.
- Draw $\ds \frac{(x-2)^2}{16}+\frac{(y-3)^2}{9}=1$.
- Draw $\ds \frac{(x-2)^2}{16}-\frac{(y-3)^2}{9}=1$ and $\ds \frac{(y-3)^2}{9}-\frac{(x-2)^2}{16}=1$.
- Draw $\ds \frac{(x-1)^2}{16}+\frac{(y-5)^2}{9}=1$ and then draw $\ds \frac{(x-1)^2}{16}-\frac{(y-5)^2}{9}=1$.
- Draw $\ds \frac{(x+2)^2}{9}+\frac{(y-4)^2}{25}=1$ and then draw $\ds -\frac{(x+2)^2}{9}+\frac{(y-4)^2}{25}=1$.
- Draw the parametric curve $x=2+3\cos t$, $y=5+2\sin t$. Make a $t,x,y$ table of points, and then graph the $(x,y)$ coordinates.
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