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-How long ago did you ask the second?
-Does it seem like she likes you or is she just being nice?
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I think she was unsure because she hardly knew you and felt uncomfortable just saying yes and going out with you but now that you have talked more and she has made more of an effort to come to you I would ask her out to the same place she told you about she will appreciate the fact that you want to take her somewhere where she is used to being and a public place and she may be more apt to accept this time. I think she was too shy and bashful to say yes but I think she will say yes this time. Tell her that you think she is a beautiful and a kind person you just want to get to know her better and see if you have some things in common if she likes you can start out as friends and just go as friend until she is ready to take it to the level of a relationship, maybe if you suggest going at her pace then she will feel more comfortable about giving you a chance. If she wasn't interested in you I doubt she would make such an effort to sit with you at lunch or come talk to you if she didn't want to be bothered at all she would go the other way, it's been three weeks since you asked her out last so now is the time to give it another try. Make sure you ask her to go to the place she told you about in Santa Monica so that she is in a familiar place and can feel more comfortable on a first date.