  We consider a BEC of rigid rotor molecules confined to quasi-2d through
harmonic trapping. The molecules are subjected to an external electric field
which polarizes the gas, and the molecules interact via dipole-dipole
interactions. We present a description of the ground state and low-energy
excitations of the system including an analysis of the mean-field energy,
polarization, and stability. Under large electric fields the gas becomes fully
polarized and we reproduce a well known density-wave instability which arises
in polar BECs. Under smaller applied electric fields the gas develops an
in-plane polarization leading to the emergence of a new global instability as
the molecules "tilt". The character of these instabilities is clarified by
means of momentum-space density-density structure factors. A peak at zero
momentum in the spin-spin structure factor for the in-plane component of the
polarization indicates that the tilt instability is a global phonon-like
instability.
