I haven't watched the video, but if you perform a http://mathworld.wolfram.com/RotationMatrix.html" by an angle \theta about the z axis on the vector {\bf r} = \left(x,y,z\right) , you get r' = r + \Delta r = \left(\cos \theta x - \sin \theta y, \sin \theta x + \cos \theta y ,z\right) . For...