I'm up for the task.

I am assigned to room A.

homework / assignment 

'Homework' is always singular. If you want to use it as plural, you can say "(homework) assignments".

allocate: 할당하다. 

quota: 할당량, Every has their own quota for this project.

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For our group project, we need someone who can take on researching the information.

take on: 일을 맡다, 채용하다

They told me not to take on any more work.

I can't take on any other task at the moment.

do vs take on 

do: 지금 당장 한다는 느낌.

take on: 맡는다는 느낌.

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I am up for the task. However, it would be better to divide up the research. 

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Good idea. You take the science part and assign someone to do the math part.

James was assigned to investigate the accident.

I assign him to be your guide.

(내가 저 사람을 가이드로 붙여줄게요.)

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shoot a video/ a photo / shot: 장면

job opportunity: 일자리 

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This is not just any hotel. 

(여기는 그저그런 호텔이 아니다.)