If I say to my English friends
What have you been doing since you have been here?
(in fact I want to know how they have been occupied) is it impolite? Why? (tense or verb)
How can I say this better?
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Possibly :) There are a lot of subtle differences. As a general rule of thumb, intersperse the sentence with conditionals, use the passive voice and specialize the verb (change "do" to "working on")
passive vs active: active adjectives, ending in –ing, express the idea that someone or something causes a certain effect. Passive adjectives, which end in –ed, express that someone or something experiences this effect.
If said aggressively, this could be interpreted as rude and accusatory (probably not from friends, but can be construed this way)
This should be said quietly with a questioning tone so as not to be confrontational. Also, small talk is considered polite before getting straight to the question, such as "how was your journey?"