The phrase "are deeply apprehensive" is correct and usable in written English.
It can be used to express a strong feeling of anxiety or concern about a situation.
Example: "The students are deeply apprehensive about the upcoming exams, fearing they may not perform well."
Alternatives: "are very anxious" or "are extremely worried."
Others are deeply apprehensive and the spectrum of responses suggests that Google's gadget has touched a nerve in a way that few technologies do.
Muslim community groups have condemned the killing of Mr. Rigby in unequivocal terms, and say that many British Muslims are deeply apprehensive over a number of incidents of hostile graffiti and invective since his death, despite appeals for calm from Prime Minister David Cameron, the archbishop of Canterbury, the Most Rev. Justin Welby, and other prominent figures.
"We are deeply apprehensive," he added.
Many people made it clear that they were deeply apprehensive about Mr. Obama, though some said they were hoping for the best.
Yet Egypt, like Saudi Arabia and other Sunni Arab states, is deeply apprehensive about a "Shia bomb," and in January, 2010, when a nuclear scientist named Massoud Ali Mohammadi was assassinated in Tehran, Egypt's largest-circulation newspaper, Al Ahram, published an article calling Dagan "Israel's superman" and "the brains" behind the killing.
"We are deeply, deeply engaged".
"It was deeply, deeply satisfying".
He is a distinctly anti-revolutionary conservative, deeply apprehensive of any grassroots challenge.
Deeply apprehensive about the merger between Time Warner and AOL in 2001, Mr Fernandes left Warner Music soon after the disastrous deal was finalised, cashing in his shares just in time.
"We're going to play for as long as we can," he announces happily, a remark greeted with deafening cheers, rather than the deeply apprehensive gulp it warrants.
