  We examine the hydrostatic stress of electrons strongly confined in a
quasi-2D quantum well in the presence of a strong perpendicular and weak
in-plane magnetic field. This introduces anisotropy into the stress tensor
which is inconsistent with the notion of the quantum Hall droplet as a simple
two-dimensional electron fluid. We show that the breaking of rotational
symmetry is a necessary but not a sufficient condition for an anisotropic
ground state stress tensor, and that the anisotropic stress originates
primarily from quantum effects. We demonstrate this by decomposing the
semiclassical trajectories of electrons in the system onto planes in phase
space which must be rotated relative to the plane of the fluid to decouple the
Hamiltonian.
