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Question 9 Question 5 Consider the curve $x = \cos(t)$, $y = \sin(t)$, $z = 0$ which is a circle of radius one inside the $x - y$ plane contained $\mathbb{R}^3$. We apply the matrix $\begin{pmatrix} 2 & 1 & 0\\ -1 & -2 & 0\\ 0 & 0 & -5 \end{pmatrix}$ to it, giving rise to an ellipse on the $x - y$ plane. a) Determine if this path moves in a clockwise or counterclockwise direction around the ellipse when $t$ increases. b) Compute the area of the ellipse which is contained in the plane. Area of ellipse is 3pi Area of ellipse is 3pi Area of ellipse is 15pi Area of ellipse is 5pi 10 pts

          Question 9
Question 5 Consider the curve $x = \cos(t)$, $y = \sin(t)$, $z = 0$ which is a circle of
radius one inside the $x - y$ plane contained $\mathbb{R}^3$. We apply the matrix
$\begin{pmatrix} 2 & 1 & 0\\ -1 & -2 & 0\\ 0 & 0 & -5 \end{pmatrix}$
to it, giving rise to an ellipse on the $x - y$ plane.
a) Determine if this path moves in a clockwise or counterclockwise direction
around the ellipse when $t$ increases.
b) Compute the area of the ellipse which is contained in the plane.
Area of ellipse is 3pi
Area of ellipse is 3pi
Area of ellipse is 15pi
Area of ellipse is 5pi
10 pts

Question 9
Question 5 Consider the curve x = cos(t), y = sin(t), z = 0 which is a circle of
radius one inside the x - y plane contained ℝ^3. We apply the matrix
< p m a t r i x >
to it, giving rise to an ellipse on the x - y plane.
a) Determine if this path moves in a clockwise or counterclockwise direction
around the ellipse when t increases.
b) Compute the area of the ellipse which is contained in the plane.
Area of ellipse is 3pi
Area of ellipse is 3pi
Area of ellipse is 15pi
Area of ellipse is 5pi
10 pts

Added by Victoria S.

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