1. Radical technology will be invented soon. (you don’t need ‘a’, unless referring to a specific ‘radical form of technology’ ‘Radical technology is both general and broad, because we don’t know what ‘kind’ of technology will exist in the future)

2. My hands were shaking with rage, when I met a racist guy.

3. It is reckless to enter the Tokyo University. (reckless = is defined as being ‘dangerous’ ‘rash’, Is it really dangerous to enter Tokyo University?;) maybe use another word, depending on what you want to say

4. I had a fight with my bf, but we reconciled the next day (‘the’ needs to be included, because ‘the’ ‘next day’ gives us a specific time frame).

5. I felt resentment, when I was deceived by fraud in China. (to be resented = to feel bitter towards a person, action or situation. If you say “I resented …..” it implies you feel bitter towards something, someone or a situation. BUT in your sentence ‘you were ‘decieved’ and as a result felt ‘you were treated badly’. So it is better to use ‘resentment’ = feeling bitter for being treated badly)

6. In new years in Japan, we go to shrines for a ritual event.

7. Applying for a patent means getting a sanction to sell new products.

8. Earthquakes are scarce in Australia.

9. Sheer stockings are easily ragged. (are easy to be ragged = is correct, but it is more natural to make ‘easy’ an adverb, since ‘to be’ can be omitted (are easy ragged = are easily ragged)

10. I speculate that Mt. Fuji will erupt this year.

I hope this helps, if you have any questions about my corrections, feel free to contact me. Great Job