  We show that any stack $\mathfrak{X}$ of finite type over a Noetherian scheme
has a presentation $X \rightarrow \mathfrak{X}$ by a scheme of finite type such
that $X(F) \rightarrow \mathfrak{X}(F)$ is onto, for every finite or real
closed field $F$. Under some additional conditions on $\mathfrak{X}$, we show
the same for all perfect fields. We prove similar results for (some) Henselian
rings.
  We give two applications of the main result. One is to counting isomorphism
classes of stacks over the rings $\mathbb{Z}/p^n$; the other is about the
relation between real algebraic and Nash stacks.
