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Do it yourself. Agencies are scams. Advertise to friends and your old highschool or local highschool.

For no solutions the determinant has to be zero...which is ad-bc in the matrix of coefficients...so solve 1-k^2=0 to find values of K such that there are no solutions

Sounds awesome...promotion prospects will be great

Very broad. What kind of science do you like. Have you talked with someone who has done the bioinformatics?

There are some rural bonded grants for medicine in some states

It would indicate value if all courses had the same quotas for students and all students applying had perfect information of job markets and decided solely based on employability + salary prospects

You will make new friends at uni regardless of who you went to school with. Only you can decide whether you value your high school friends more or your perception of the other uni. I had 2 friends from school go to uni together and end up working together in the same eng firm

If you're going to do a gap half year try to plan your degree so it takes 6 months longer and you end up graduating with the following year cohort. You can effectively have 4 semesters where you only take 3 subjects instead of 4