 Solution

Use column vectors in a right-handed frame, and interpret clockwise as viewed from the positive $x$-axis towards the origin. The rotation matrix fixes $e_x$ and sends $e_y$ towards $-e_z$. With $q=1/\sqrt{2}$, its images of the basis vectors giveThe transverse block is the planar rotation through $-\pi /4$. Viewing from the other end of the axis reverses the meaning of clockwise and replaces $R$ by $R^T$; the viewpoint is not specified in the paper.