  We give an account of well known calculations of the RO(Q)-graded coefficient
rings of some of the most basic Q-equivariant cohomology theories, where Q is a
group of order 2. One purpose is to advertise the effectiveness of the Tate
square, showing it has advantages over the slice spectral sequences in
algebraically simple cases. A second purpose is to give a single account
showing how to translate between the languages of different approaches. [v2
corrects some typos and adds some thanks and references, v3 corrects a few more
typos].
