Answer: In 4346, use a CAS to solve the given system

Chapter 8, Problem 46

(choose chapter or problem)

If a vector \(\mathbf{a}=\overrightarrow{O P}=\langle x, y\rangle \text { in } R^{2}\) is rotated counterclockwise about the origin through an angle \(\theta\), then the components of the resulting vector \(\mathbf{b}=\overrightarrow{O P_{1}}=\left\langle x_{1}, y_{1}\right\rangle\) are given by B = MA. where

\(\mathbf{A}=\left(\begin{array}{l} x \\ y \end{array}\right), \mathbf{B}=\left(\begin{array}{l} x_{1} \\ y_{1} \end{array}\right) \text {, and } \mathbf{M}=\left(\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right)\).

The \(2\ \times\ 2\) matrix M is called a rotation matrix. See Figure 8.1.1. In Problems 45-48, find the resulting vector b if the given vector \(\mathbf{a}=\overrightarrow{O P}=\langle x, y\rangle\) is rotated through the indicated angle.

\(\mathbf{a}=\langle-2,4\rangle, \theta=\pi / 6\)