The phrase "strongly care" is grammatically correct and can be used in written English.
It is often used to express a strong feeling or concern towards something or someone. Here is an example of how it can be used in a sentence: "I strongly care about the environment and believe we should all make an effort to reduce our carbon footprint."
I had to forcefully make him understand that I strongly cared for these young women.
An example item is 'This doctor strongly cares about your health' (5-point Likert scale: completely disagree = 1 to completely agree = 5).
If she strongly cares about the environment, for example, and you say something about not believing in climate change, then she's going to reject you.
"Google underestimates how strongly people care about privacy and underestimates governments' willingness to take action," said Marc Rotenberg, executive director of the Electronic Privacy Information Center, a privacy rights group.
This may also be why I am slightly skeptical of proposals, in the wake of Tucson, to do away with the divided-by-party seating at the State of the Union: sometimes it's helpful to know what the teams are, and how strongly they care about certain moves and plays.
The students reacted strongly, each caring deeply about his or her alternative fate.
Most people also care strongly about candidates' caste and religion.
Indian Tamils care strongly about the issue, so there is an opportunity both to attack the ruling Congress party and just possibly to influence foreign policy.
For those of us in Britain who care strongly about tackling the injustice of extreme poverty, the prime minister will be in an incredible position, the opportunities inherent in which we must maximise.
"They care strongly about justice and the problems faced by their society and are typically engaged in some kind of civic activity at school, at work or in their communities".
