Vanderbilt, Duke, and Georgia Tech

I’m a rising senior in high school at a small private institution. My strengths are math and science, and I am planning on majoring in some type of engineering (right now I am thinking something like computer or electrical or maybe even computer science) and maybe double majoring in econ or something if I have enough hours going in. What do you think my chances of getting in are?
GPA: 4.75 weighted (that is all that we have)
ACT: 36 composite
SAT: n/a
AP’s: US History-4, BC Calculus-5, Physics C:Mechanics-5, English Lang and Comp-4
Next year, I will be taking the following AP’s :Comp Sci, Stat, Physics:Electricity and Magnetism, and Government

Extracurricular- 2 Sports(Bowling and Soccer)Eagle Scout,Volunteer stuff is good, math contests

Letter of Recommendation- Math teacher will write me a great one
History teacher will write me a good one but probably not as good as my math one

You should calculate your unweighted GPA because that is what most selective colleges will do. Consider also Olin, Carnegie Mellon, Emory, Harvey Mudd