We have investigated the low-energy states of N-11 by the resonant elastic-scattering method in inverse kinematics using a C-10 beam and a (CH2)(n) target at the CYCLONE facility at Louvain-la-Neuve. Recoil protons were detected at laboratory angles theta(lab)=5.2 degrees-18.3 degrees in a Delta E-E detector system. The absolute C-10+p elastic cross-section data were analyzed in the R-matrix framework. We found N-11 to be unbound with respect to proton emission by 1.54 +/- 0.02 MeV, with a decay width of 0.83 +/- 0.03 MeV. These results are used to calculate the two-proton decay width of the O-12 ground state.