Final answer:
The speaker of the quote is Ophelia from Shakespeare's play 'Hamlet'. The flowers she mentions symbolize remembrance and thoughts, reflecting her mental state.
Step-by-step explanation:
The correct speaker for the quotation "There's rosemary, that's for remembrance; and here's pansies, that's for thoughts," is Ophelia from William Shakespeare's play Hamlet.
This line from Act 4, Scene 5, is part of a larger speech where Ophelia is distributing flowers that symbolize various things such as remembrance, thoughts, and infidelity, reflecting her descent into madness after her father's death and Hamlet's erratic behavior. The flowers serve as poignant symbols of her inner turmoil and the tragic themes of the play.