GPA

So I just switched schools senior year from a competitive private school to a competitive public school. My transcript shows that I have taken the most difficult course load from the private school, and this year I am taking the most difficult course load for this new public school. However, at this new school there are many more APs available for students to take, and their GPA scaling is indicative of that with a different scale. At my old school they had a quartile system in which I was well in the top 25% of students. At this old school however, my GPA would not be very high as I have not taken near as many APs to be competitive here even though I was very competitive at my old school. This school has a ranking system and I would be fairly low even though had I attended all four years I would be ranked much higher. I have had all As except for a B in one semester of Advanced Physics and another B in one semester of AP World History. Am I still at the acceptable GPA range for schools like Yale?

Yes. You grades/course selections at your old school will be viewed in the context of your old school, not your new one.