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In ArcGIS 10.1, for what tools does Environments actually work?

As a new user, often I have used "active" (that is, not grayed out and non-functional) Environments when using ArcToolbox Tools and the operation is non-responsive. I wish I documented for my own record what I have seen along the way, but have not, still being somewhat confused as to whether it is because I am doing something wrong. Following are two recent examples.

  1. Using a raster, I have seen where

    Spatial Analyst > Extract by Polygon > Environments > Raster Analysis and changing the cell size will not change the cell size;

and

  1. using a raster

    Data Management > Resample > Environments > Raster Analysis > Mask will change the cell size but not mask.

Since the combination of operations that are not allowed by ArcGIS do not result in grayed out inactive buttons or a warning message, is there some list that tells what Environment operations can and can't be done with the various ArcToolbox Tools?