  We present a class of spacetime rotations that preserve a proportion of
spacetime supersymmetry. We then give the rules for superposing these rotations
with various branes to construct rotating brane solutions which preserve exotic
fractions of supersymmetry. We also investigate the superposition of rotations
with intersecting branes at angles and we find new rotating intersecting branes
at angles configurations. We demonstrate this with two examples of such
solutions one involving intersecting NS-5-branes on a string at $Sp(2)$ angles
superposed with fundamental strings and pp-waves, and the other involving
intersecting M-5-branes on a string at $Sp(2)$ angles superposed with membranes
and pp-waves. We find that the geometry of some of these solutions near the
intersection region of every pair of 5-branes is $AdS_3\times S^3\times
S^3\times \bE$ and $AdS_3\times S^3\times S^3\times\bE^2$, respectively. We
also present a class of solutions that can be used for null string and M-theory
compactifications preserving supersymmetry.
