  We calculate the Hall viscosity and the nonlocal (i.e., dependent on wave
vector $\bm q$) Hall conductivity of "gapped graphene" (a non-topological
insulator with two valleys) in the presence of a strong perpendicular magnetic
field. Using the linear-response theory at zero temperature within the Dirac
approximation for the Landau levels, we present analytical expressions for both
valley and total Hall viscosity and conductivity up to $\bm q^2$ at all
frequencies. Although the final formulas for total Hall viscosity and
conductivity are similar to the ones previously obtained for gapless graphene,
the derivation reveals a significant difference between the two systems. First
of all, both the Hall viscosity and the Hall conductivity vanish when the Fermi
level lies in the gap that separates the lowest Landau level in the conduction
band from the highest Landau level in the valence band. It is only when the
Fermi level {\it is not} in the gap that the familiar formulas of gapless
graphene are recovered. Second, in the case of gapped graphene, it is not
possible (at least within our present approach) to define a single-valley Hall
viscosity: this quantity diverges with a strength proportional to the magnitude
of the gap. It is only when both valleys are included that the diverging terms,
having opposite signs in the two valleys, cancel out and the familiar result is
recovered. In contrast to this, the nonlocal Hall conductivity is finite in
each valley. These results indicate that the Hoyos-Son formula connecting the
Hall viscosity to the coefficient of $q^2$ in the small-$q$ expansion of the
$q$-dependent Hall conductivity cannot be applied to each valley, but only to
the system as a whole. The problem of defining a "valley Hall viscosity"
remains open.
