The cap in the hat: unoriented 2D strings and matrix(-vector) models

We classify the possible bosonic and type 0 unoriented open and closed string theories in two dimensions, and find their dual matrix(-vector) models. There are no Rp(2) R-R tadpoles in any of the models, but many of them possess a massless tachyon tadpole. Thus all the models we find are consistent two-dimensional string vacua, but some get quantum corrections to their classical tachyon background. Where possible, we solve the tadpole cancellation condition, and find all the tachyon tadpole-free theories.