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I am trying to understand a couple related questions that I missed. I want to understand...

I am trying to understand a couple related questions that I missed. I want to understand the whole picture of it, because I am still struggling with resonance because I am having problems understanding these.  

Why is the hydroxyl oxygen atom of the carboxylic acid functional group sp2?

What are the hybridizations of the oxygen and nitrogen atoms in 1-(3-methoxyphenyl)-N,N-dimethylamine? (sorry it won't let me copy and paste the structure from chemsketch, I tried)

I had put down sp3, sp3, but they are not. Are they sp2 as well? Why?

Does being sp2 with the lone pair in the pi orbital what makes resonance possible? Or does it just make it more likely? Can sp3 hybridized atoms participate in resonance? Why or why not?

Finally, how can this help to define what resonance happens, where, and if it contributes to the overall structure? When carbon is sp3 and participates in resonance it tends to develop a charge, is that why you are supposed to "keep the carbons happy?" Because sp3 hybridized atoms shouldn't participate in resonance?

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