What constitutes a strong female character in a movie?

I’ve noticed that movies have tended to shift from one extreme to another when showing females. Either they were parts with minor speaking roles almost like arm candy for the male leads. Nearly helpless without a man. Then the trend shifted to the extreme where you have movies about women kicking ass all over the place, often with martial arts moves. Often unstoppable by any male. As a result another opposing female has to be introduced to stop her.

This new “strong woman” role is basically an effort on the part of Hollywood to cater to feminism in some fucked up way by turning women into men.

But this later option strikes me as a cheap move on the part of Hollywood. It kind of reminds me of that line from the movie As Good As it Gets where she asks “How do you write women so wel?l” and he replies “I think of a man and then take away…” only in this version of that answer it goes something like this:

“I think of a man and then I add tighter clothes, invincibility against anything male and more kicking.”

But to me this seems just as sexist as the minor speaking part/arm candy/helpless-without-a-man style female roles that existed before this strong woman revolution. I’ve never actually met a female in real life that fits either extrmeme.
So it annoys me when these actresses get interviewed and say things like:

“I’m glad to play this character because she’s such a postive role model for young girls by being such a strong female.”

What? By telling her she can grow up to be Bruce Lee? Why don’t you also throw in a coupon code for a sex change while you’re at it?

I have no problem this the occasional female character that can kick ass. Don’t misread me. What I have a problem with are these two extremes where you either get one or the other. Either you get Megan Fox in Transformers who is just arm candy for the male lead or you get Charlies Angels.