  We precisely test scale invariance and local thermal equilibrium in the
hydrodynamic expansion of a Fermi gas of atoms as a function of interaction
strength. After release from an anisotropic optical trap, we observe that a
resonantly interacting gas obeys scale-invariant hydrodynamics, where the mean
square cloud size $\langle{\mathbf{r}}^2\rangle=\langle x^2+y^2+z^2\rangle$
expands ballistically (like a noninteracting gas) and the energy-averaged bulk
viscosity is consistent with zero, $0.005(0.016)\,\hbar\,n$, with $n$ the
density. In contrast, the aspect ratios of the cloud exhibit anisotropic
"elliptic" flow with an energy-dependent shear viscosity. Tuning away from
resonance, we observe conformal symmetry breaking, where
$\langle{\mathbf{r}}^2\rangle$ deviates from ballistic flow.
