选whose,因为whose+名词activity引导定语从句.而且定语从句的谓语动词是is sending ,是单数形式.
注意：whose+名词引导定语从句时,所修饰的先行词和whose后的名词之间有所有关系.在这句话中我们可以这么解释：people's activity.
又如：Li Ming is the boy whose pronunciation is the best in my class.
其他三个选项后面不接名词,而是直接来引导定语从句的.
Li Ming is the boy who has cleaned the room.
This is the book which/that I bought yesterday.