$1\mathrm{.}4$

Write a function that computes the rotation matrix $R$ from an axis $$ and an angle $.$ Then

use that function to find the following rotation matrix:

hat$()=\left[\begin{array}{c}\frac{\sqrt[\phantom{2}]{2}}{2}\\ 0\\ \frac{\sqrt[\phantom{2}]{2}}{2}\end{array}\right],=\frac{}{4}$

Prove that your result is a rotation matrix.