嬴政的老婆丽姬:Tom had finished his homework at the end of last month.

用at the end of不可以,只能是by the end of
at the end of
在...结尾,在....末端
by the end of
到...末

at the end of 是个时间点,一般用过去时态
by the end of 是到...时间为止,一般用完成时态

应该可以吧。
你说的是BY THE END OF吧……
By the end of last month, Tom had finished his homework.
By the end of＋句子。

Tom had finished his homework at the end of last month.
汤姆在上个月的月底完成了他的作业。

可以是at the end of 吗?

可以 那么这句话就要改成：
Tom had finished his homework at the end of the month.
汤姆在这个月底完成了他的作业。

（这里month前面要加"the"要不然就成了Tom had finished his homework at the end of month.）

它和by the end you 有什么不同?
at the end of the month (在月底的时候）
by the end of the month (到月底的时候)

Tom had finished his homework at the end of last month.
汤姆在到月底的时候完成了他的作业。

又如：
at the end of the year (在年底的时候）
by the end of the year (到年底的时候)

His annual salary added up to about $30 000 at the end of the year.
他的年收入在年底的时候总共差不多$30 000。

在这里，是指在什么什么（时候）的最后 - 也就是那个时候已经到了，发生了什么事 先前是完全没有计划的 在年底 就正好发现年收入是三万

要是用 by the end of
就是：
His annual salary added up to about $30 000 by the end of the year.
他的年薪到年底总计到了$30 000。

不知道这么说懂吗~~是不是太复杂了