Let \(f\) be the transformation of \(\mathbb{R}^{2}\) given…

Let \(f\) be the transformation of \(\mathbb{R}^{2}\) given by rotating \(80^{\circ}\) counterclockwise around the origin. Find the standard matrix for \(f\) and then use that to find where the point \(\left(5,4\right)\) gets sent under this rotation. (As \(80^{\circ}\) is not a special angle, you will have to use decimal approximations.)

Let \(\mathcal{B}=\left\{\begin{bmatrix}2\\-1\end{bmatrix},\…

Let \(\mathcal{B}=\left\{\begin{bmatrix}2\\-1\end{bmatrix},\begin{bmatrix}7\\-3\end{bmatrix}\right\}\) and \(\mathcal{B}^{\prime}=\left\{\begin{bmatrix}5\\4\end{bmatrix},\begin{bmatrix}1\\1\end{bmatrix}\right\}\). Find the transition matrix \(P_{\mathcal{B}\to\mathcal{B}^{\prime}}\).