(a) Find, with justification, the matrix, with respect to the standard basis of $\mathbb{R}^{2}$, of the rotation through an angle $\alpha$ about the origin.

(b) Find the matrix, with respect to the standard basis of $\mathbb{R}^{3}$, of the rotation through an angle $\alpha$ about the axis containing the point $\left(\frac{3}{5}, \frac{4}{5}, 0\right)$ and the origin. You may express your answer in the form of a product of matrices.