【正确答案】 C

【答案解析】[理由] 本句测试动词convince的用法：
convince sb that... 说服某人相信……
convince sb of sth 说服某人相信某事
[例] You need to convince him of your passion for the job.
(你必须让他相信你对这份工作的热忱。)
convince之后若无人作宾语时，则须用被动语态，形成下列用法：
be convinced that... 相信……(=be sure that...)
be convinced of sth 相信某事(=be sure of sth)
[例] Mrs. Jackson was convinced of her daughter's musical talent.
(杰克逊太太深信女儿具有音乐天赋。)
I am convinced that the event will be a success.
(我深信这次活动一定会顺利成功。)
原句中，空格后因为只有that从句，并没有表“人”的名词作宾语，故不可能直接置convince，应使用被动语态to be convinced(被说服相信的)，故(C)应为正选。
[注意]
convincing是现在分词，可作形容词，表“令人信服的”。
[例] His words are not convincing.
(他的话不值得相信/不具说服力。)