投(tóu) - to throw, to cast, to invest, to submit in Mandarin

投 (tóu) starts from a hand throwing something and fans out from there. Physically it is to throw or cast: 投球 to throw a ball, 投进 to throw something in. Everything else in the word family is that same gesture applied to money, paper or trust.

The high frequency compounds are worth learning as blocks. 投票 is to vote, literally to cast a ballot. 投资 is to invest, to throw capital at something. 投入 is to put in or to be absorbed in. 投稿 is to submit a manuscript. In each one the sense of directing something away from yourself towards a target is still visible.

The trap is expecting 投 to work like a general purpose throw in conversation. For chucking something across a room, Chinese uses 扔 (rēng); for dropping or discarding, 丢 (diū). 投 alone is mostly restricted to sport, ballots and set compounds, so a learner who says 把书投给我 will be understood but will sound like a sports commentator.