Support Battery Draining Quickly/Phone Getting Hot

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http://androidforums.com – I just got a new Galaxy Nexus yesterday, and the battery is just dying so fast, and phone is getting really hot. Why is that? I turned off the 4G/LTE preferred setting. What else can I do? The battery settings say that the screen is using 62% of my battery (and the screen has barely even been on). (General)