My judge solution to Overlapping Maps from UChicago's 2013 Invitational Contest.

maps.cpp

#include <iostream>
#include <cstdio>
#include <cassert>
#include <cmath>

using namespace std;

/*
X' = ASX + O
(AS-I)X+O = 0
*/

#define EPS 1e-9

int main() {
  for(int t = 1; ; t++) {
    int W, H, X, Y, S, R;
    cin >> W >> H >> X >> Y >> S >> R;
    if(!W) break;

    double theta = 3.14159265358979 * R / 180;

    double A[2][2];
    A[0][0] = cos(theta) * S / 100 - 1;
    A[0][1] = -sin(theta) * S / 100;
    A[1][0] = sin(theta) * S / 100;
    A[1][1] = cos(theta) * S / 100 - 1;

    double det = A[0][0] * A[1][1] - A[0][1] * A[1][0];
    assert(det > EPS);
    
    printf("%.2f %.2f\n", (A[0][1] * Y - A[1][1] * X) / det,
                          (A[1][0] * X - A[0][0] * Y) / det);
  }
  return 0;
}