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correlation question

First: The question is really not related to R.

What you can find very easly in books or in the internet:
The correlation coefficient is invariant under a linear transformation
(and the proof) 
#E.g. 
library(rrcov)
data(brain)
cor(brain)
cor(scale(brain))  #Is the same, BUT
cor(log(brain))    #Is VERY different.

Best,
Matthias