You should drop the course as soon as possible.
你应该尽快逃课。
I'd appreciate it if you can contact me as soon as possible.
如果你能尽快联系我，我会很感激。
Government should also draft relevant regulations as soon as possible.
政府也应尽快起草相关法规。
I hope you can make an investigation into this matter as soon as possible.
我希望您能尽快调查这一问题。