Can you explain the members of AIRealMatrix?

This is a pretty standard transformation matrix structure. a, b, c & d are the usual 2 x 2 matrix that indicates rotation & scaling. tx & ty are the translation to the point around which the scaling & rotation are performed (usually its a translation back to the origin unless you have a good reason otherwise). You're probably better off looking at Wikipedia or Wolfrum if you need more explanations on this but the good news its very common so there should be a lot of useful explanations -- its really outside of the scope of this forum.