Bob - I read somewhere that the concrete floor was true for yesterday's batteries, but doesn't matter anymore.
Gordie - do not put a tarp on it. If you use a tarp (and I'm assuming when you say tarp you mean the blue plastic things), then hang it above it so that it is not touching. If you want a cover, get an ADCO or something similar from Camping World or elsewhere - they can "breathe" and allow it to NOT retain moisture under it.
I'm a big proponent of covering them somehow when not in use. If there happens to be an undetectable leak somewhere, at least when it's covered, rain won't get in 90% or more of the time. There may be a problem with a cover scratching (especially on fiberglass). I keep my cinched down tight so the wind can't blow it around and haven't had problems.
Again, please don't cover it tight with a blue tarp.