to be honest, i'm not sure what's going on in this thread. either the OP is taking the piss or he is earnest but enormously ill-informed and ill-prepared to be taking an advanced theory class. i don't know which but either makes this kind of pointless.
that said, as to the OP's OQ: a piece of music (classical or not) can be in a key/mode and yet over the course of the piece multiple tonal centers can be employed. if the tonal center is 'strong' enough, you've basically changed key a/o mode. it's really that simple.
as for the business about knowing what A sounds like 'cause you play it on your guitar, well, i've been playing guitar for 30 years and i don't know what A 'sounds like' on my gtr. all in all, i suspect a wind up. if not, then i suggest the OP start with a music appreciation class before taking any theory. for starters, a large fraction (probably a majority) of classical pieces don't involve an orchestra at all.
cheers (or not)
"Patsy had the drug tolerance of Keith Richards and the moral rectitude of Brian Jones." - Dr. Walter Bishop, "Fringe"