apologies
n.
道歉，认错，愧悔( apology的名词复数 );
例句:
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So, apologies to them for my sudden elevation.
来自BBC
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With apologies to my old history teacher, who needs history lessons?
这话对不住我亲爱的历史老师，不过有谁需要历史课呢？
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First off, huge apologies for last month's confusing report.
首先,要对上个月那篇交代不清的报道表示深深的歉意.
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Union officials made no apologies for the threatened chaos.
工会干部们对于迫在眉睫的混乱局面不予道歉。
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President Obama also offered his apologies for the study.
来自VOA
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This clip covers making apologies and other business-related language.
来自BBC