Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2015 / Paper 1 / 5 / c

Use the lower antisymmetric block shown in the original PDF. Write $M=\mathrm{diag}(aK,bJ)$ withPowers preserve the block structure. Splitting the matrix exponential series into even and odd powers gives $e^{aK}=I\cosh a+K\sinh a$. For the other block, the matrix exponential when the square is minus the identity gives $e^{bJ}=I\cos b+J\sin b$. ThereforeThe upper block is hyperbolic and the lower block is a rotation. The transcription's altered last row and hyperbolic functions in the lower block would describe a different problem.