  We consider a "symmetric" quantum droplet in two spatial dimensions, which
rotates in a harmonic potential, focusing mostly on the limit of "rapid"
rotation. We examine this problem using a purely numerical approach, as well as
a semi-analytic Wigner-Seitz approximation (first developed by Baym, Pethick et
al.) for the description of the state with a vortex lattice. Within this
approximation we assume that each vortex occupies a cylindrical cell, with the
vortex-core size treated as a variational parameter. Working with a fixed
angular momentum, as the angular momentum increases and depending on the atom
number, the droplet accommodates none, few, or many vortices, before it turns
to center-of-mass excitation. For the case of a "large" droplet, working with a
fixed rotational frequency of the trap $\Omega$, as $\Omega$ approaches the
trap frequency $\omega$, a vortex lattice forms, the number of vortices
increases, the mean spacing between them decreases, while the "size" of each
vortex increases as compared to the size of each cell. In contrast to the
well-known problem of contact interactions, where we have melting of the vortex
lattice and highly-correlated many-body states, here no melting of the vortex
lattice is present, even when $\Omega = \omega$. This difference is due to the
fact that the droplet is self-bound. Actually, for $\Omega = \omega$, the
"smoothed" density distribution becomes a flat top, very much like the static
droplet. When $\Omega$ exceeds $\omega$, the droplet maintains its shape and
escapes to infinity, via center-of-mass motion.
