for your hair, you could try a really classy ponytail. The low kind where your hair is parted and another section of hair is wrapped around the elastic, or you could do a simple up do for pref. Anything sleek and pulled back (without alot of wispys in your face) should hold up pretty well and look nice. As far as make-up goes, I think a couple of brands make liquid mattifier that you can put on before your make-up that can keep you dry, and I use this cover-girl pocket powder these days that keeps me pretty dry in the GA heat. Those oil absorbing sheets rock. A couple of little things packed in a small purse or kept by your Rho Chi can go a long way in between rounds. (We have outdoor rush in August)
as far as strapless goes, that would be a question for an LSU aquainted person to answer. we're pretty laid back here, so a strapless sundress or evening dress would be acceptable. A strapless-corset type top would probably look a little too clubby
good luck!!!!!
