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.)