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1) Do we have art class tomorrow?
2) Will we have art class tomorrow?
If I have to ask if we have art class tomorrow or not, I'll choose the first one because the present tense axiliary 'do' specifies a general idea or a simple fact. For example,
Possible answers from the questions:
Yes, I have art class tomorrow. (OK)
Yes, I will have art class tomorrow. (OK, but-)
Auxiliary 
Linear Mode
