  We investigate the collective excitations of a harmonically trapped
two-dimensional Fermi gas from the collisionless (zero sound) to the
hydrodynamic (first sound) regime. The breathing mode, which is sensitive to
the equation of state, is observed at a frequency two times the dipole mode
frequency for a large range of interaction strengths and temperatures, and the
amplitude of the breathing mode is undamped. This provides evidence for a
dynamical SO(2,1) scaling symmetry of the two-dimensional Fermi gas. Moreover,
we investigate the quadrupole mode to measure the shear viscosity of the
two-dimensional gas and study its temperature dependence.
