My teacher's rich knowledge of science my decision study science.
A. influenced；to
B. influenced；on
C. has influenced；with
D. influences；on
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(答案→)A. influenced；to
B. influenced；on
C. has influenced；with
D. influences；on
解析：根据句子结构可知，第一个空要填动词，作谓语；第二个空要填入不定式符号to，动词不定式短语作后置定语。