Rotational Transformations
Linear Transformations alter the coordinate system such that the origin stays the same. So, they are useful for representing rotations using matrices. In order to represent a rotation with angle $\varphi$, you can use the matrice below:
$$ \begin{bmatrix} cos \varphi & -sin \varphi \\sin \varphi & cos \varphi \end{bmatrix} $$