  We present kinematic and metallicity profiles for the M31 dwarf elliptical
(dE) satellite galaxies NGC 147 and NGC 185. The profiles represent the most
extensive spectroscopic radial coverage for any dE galaxy, extending to a
projected distance of eight half-light radii (8 r_eff = 14'). We achieve this
coverage via Keck/DEIMOS multislit spectroscopic observations of 520 and 442
member red giant branch stars in NGC 147 and NGC 185, respectively. In contrast
to previous studies, we find that both dEs have significant internal rotation.
We measure a maximum rotational velocity of 17+/-2 km/s for NGC 147 and 15+/-5
km/s for NGC 185. The velocity dispersions decrease gently with radius with an
average dispersion of 16+/-1 km/s for NGC 147 and 24+/-1 km/s for NGC 185. Both
dEs have internal metallicity dispersions of 0.5 dex, but show no evidence for
a radial metallicity gradient. We construct two-integral axisymmetric dynamical
models and find that the observed kinematical profiles cannot be explained
without modest amounts of non-baryonic dark matter. We measure central
mass-to-light ratios of ML_V = 4.2+/-0.6 and ML_V = 4.6+/-0.6 for NGC 147 and
NGC 185, respectively. Both dE galaxies are consistent with being primarily
flattened by their rotational motions, although some anisotropic velocity
dispersion is needed to fully explain their observed shapes. The velocity
profiles of all three Local Group dEs (NGC 147, NGC 185 and NGC 205) suggest
that rotation is more prevalent in the dE galaxy class than previously assumed,
but is often manifest only at several times the effective radius. Since all dEs
outside the Local Group have been probed to only inside the effective radius,
this opens the door for formation mechanisms in which dEs are transformed or
stripped versions of gas-rich rotating progenitor galaxies.
