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A high-statistics study by the Columbia-Chicago-Fermilab-Rochester Collaboration of opposite-sign dimuon events induced by neutrino-nucleon scattering at the Fermilab Tevatron is presented. A sample of 5044 [nu][sub [mu]] and 1062 [bar [nu]][sub [mu]] induced [mu][sup [minus plus]][mu][sup [plus minus]] events with [ital P][sub [mu]1][ge]9 GeV/[ital c], [ital P][sub [mu]2][ge]5 GeV/[ital c], 30[le][ital E][sub [nu]][le]600 GeV, and [l angle][ital Q][sup 2][r angle]=22.2 GeV[sup 2]/[ital c][sup 2] is observed. The data support the slow-rescaling model of charm production with a value of [ital m][sub [ital c]]=1.31[plus minus]0.24 GeV[sup 2]/[ital c][sup 2]. The first measurement of the [ital Q][sup 2] dependence of the nucleon strange quark distribution [ital xs]([ital x]) is presented. The data yield the Cabibbo-Kobayashi-Maskawa matrix element [vert bar][ital V][sub [ital c][ital d]][vert bar]=0.209[plus minus]0.012 and the nucleon fractional strangeness content [eta][sub [ital s]]=0.064[sub [minus]0.007][sup +0.008].