Describe a coordinate (not point) rotation about the third axis of a Cartesian coordinate system by If for positive angles the rotation is clockwise when looking along the axis of rotation towards plus infinity, the coordinate system is right handed. Describe a Lorentz transformation by $$ \begin{array}{*{20}{c}} {{{{x'}}^{1}} = {{x}^{1}}\cos \varphi + {{x}^{2}}\sin \varphi } \\ {{{{x'}}^{2}} = - {{x}^{1}}\sin \varphi + {{x}^{2}}cos\varphi .} \\ \end{array} $$ (4a) .