Chapter 2.2, Problem 49E

(a)

To determine

To find the function $f\left(t\right)$ and graph it for $0\le t\le \frac{\pi }{2}$ for linear transformation $T\left(\overrightarrow{x}\right)=\left[\begin{array}{cc}2& 2\\ 1& -4\end{array}\right]\overrightarrow{x}$

(b)

To determine

To find a number $c$ with $0\le c\le \frac{\pi }{2}$ such that $f\left(c\right)=0$ for linear transformation $T\left(\overrightarrow{x}\right)=\left[\begin{array}{cc}2& 2\\ 1& -4\end{array}\right]\overrightarrow{x}$

(c)

To determine

To find a perpendicular unit vectors ${\overrightarrow{v}}_1$ and ${\overrightarrow{v}}_2$ in $R^2$ such that the vectors $T\left({\overrightarrow{v}}_1\right)$ and $T\left({\overrightarrow{v}}_2\right)$ are also perpendicular to each other