  Using the coarse-grain averaged hydrodynamic approach, we calculate all low
energy transverse excitation spectrum of a rotating Fermi superfluid containing
vortex lattices for all regimes along the BEC-BCS crossover. In the fast
rotating regime, the molecular BEC enters into the lowest Landau level, but the
superfluid in the unitarity and the BCS regimes occupies many low-lying Landau
levels. The difference between the breathing mode frequencies at the BEC and
unitarity limit shrinks to zero as the rotation speed approaches the radial
trap frequency, in contrast to the finite difference in the non-rotating
systems.
