核心问题
take note of 与 take a note of 这两个短语意思是否相同？
词典解答
take note of 意为“注意(到)”:
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A detective is trained to take note of people and things. (DAI) 侦探受过训练,善于注意人和事。
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He took note of the change in her appearance. (Chambers) 他注意到了她外表的变化。take a note (notes) of 意为“做笔记”“把……记录下来”：
Did you take a note of the lecture? 你对这次讲课做笔记了吗?