Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2021 / Paper 1 / 5 / c / Solution

With the same right-handed active rotation convention as $R_z$, the $y$ direction is fixed, ${\mathbf{e}}_z$ rotates towards ${\mathbf{e}}_x$, and ${\mathbf{e}}_x$ towards $-{\mathbf{e}}_z$. ThereforeIts columns give the images of the three Cartesian unit vectors, which also makes the signs of this rotation matrix explicit.