Final answer:
The dangling modifier in the sentence is 'even when lying down', as it incorrectly modifies 'the rocking sensation' instead of the person feeling the sensation.
Step-by-step explanation:
The sentence 'For a couple of days after the end of my cruise, the rocking sensation persisted even when lying down' contains a dangling modifier. A dangling modifier is a word or phrase that modifies a word not clearly stated in the sentence. In this case, the modifier 'even when lying down' seems to modify 'the rocking sensation', which cannot lie down. The phrase should clearly be connected to the person feeling the sensation. To correct the sentence, it should be rephrased to clarify that it is the person who is lying down and experiencing the sensation, such as 'For a couple of days after the end of my cruise, I felt a rocking sensation even when I was lying down.'